Combined fit of spectrum and composition data as measured by the Pierre Auger Observatory Armando di Matteo a for the Pierre Auger Collaboration b a INFN and Department of Physical and Chemical Sciences, University of L’Aquila, L’Aquila, Italy E-mail: armando.dimatteo@aquila.infn.it b Observatorio Pierre Auger, Av. San Martín Norte 304, 5613 Malargüe, Argentina E-mail: auger_spokespersons@fnal.gov Full author list: http://www.auger.org/archive/authors_2015_06.html The 34th International Cosmic Ray Conference, 30 July–6 August, 2015 The Hague, The Netherlands Armando di Matteo (Pierre Auger Collaboration) Combined fit of Auger spectrum and composition data 34th ICRC, The Hague (2015) 1 / 14
Outline Introduction 1 The models (sources, propagation, air interactions) The data (energy spectrum and X max ) Results 2 Best fit and second local minimum Dependence on propagation models, systematics, and air interaction models Conclusions 3 Armando di Matteo (Pierre Auger Collaboration) Combined fit of Auger spectrum and composition data 34th ICRC, The Hague (2015) 2 / 14
The sources We try to fit Pierre Auger Observatory data on UHECR spectrum and composition to a simple astrophysical scenario: Identical sources homogeneously distributed in a comoving volume Injection consisting only of 1 H, 4 He, 14 N and 56 Fe nuclei (approximately equally spaced in ln A ) Power-law spectrum with rigidity-dependent broken exponential cutoff � − γ � E J 0 p i , E / Z i < R cut d N inj , i E 0 = � − γ � � � d E E E J 0 p i exp 1 − , E / Z i > R cut E 0 Z i R cut Six free parameters ( J 0 , γ, R cut , p H , p He , p N ); p Fe = 1 − p H − p He − p N Armando di Matteo (Pierre Auger Collaboration) Combined fit of Auger spectrum and composition data 34th ICRC, The Hague (2015) 3 / 14
The propagation Propagation potentially strongly sensitive to: ◮ Photodisintegration cross sections (esp. into α particles) ◮ Extragalactic background light spectrum (esp. in the far IR) We used: SPG SimProp , PSB cross sections, Gilmore 2012 EBL model SPD SimProp , PSB cross sections, Domínguez 2011 EBL model STG SimProp , TALYS cross sections, Gilmore 2012 EBL model CTG CRPropa, TALYS cross sections, Gilmore 2012 EBL model CTD CRPropa, TALYS cross sections, Domínguez 2011 EBL model CGD CRPropa, Geant4 cross sections, Domínguez 2011 EBL model For details, see R. Alves Batista, D. Boncioli, A. di Matteo, A. van Vliet and D. Walz, Effects of uncertainties in simulations of extragalactic UHECR propagation, using CRPropa and SimProp , prepared for submission to JCAP (coming soon on arXiv) We neglect magnetic fields → 1D propagation Armando di Matteo (Pierre Auger Collaboration) Combined fit of Auger spectrum and composition data 34th ICRC, The Hague (2015) 4 / 14
Interactions in the atmosphere X max distributions for each A computed from CONEX simulated showers assuming: ◮ EPOS-LHC ◮ Sibyll 2.1 ◮ QGSJet II-04 Distributions fitted to a Gumbel parametrization (JCAP 1307 (2013) 050, arXiv:1305.2331 ) p ( X max | µ, σ, λ ) = λ λ exp ( − λ z − λ exp ( − z )) σ Γ( λ ) where z = X max − µ σ ( µ, σ, λ = quadratic functions of ln A and log 10 ( E / E 0 ) ) Distributions multiplied by detector acceptance and convoluted with detector resolution Armando di Matteo (Pierre Auger Collaboration) Combined fit of Auger spectrum and composition data 34th ICRC, The Hague (2015) 5 / 14
The data Fit only above 10 18 . 7 eV The spectrum (ICRC 2013, arXiv:1307.5059 ): ◮ log 10 ( E / eV ) bins [ 18 . 7 , 18 . 8 ] , [ 18 . 8 , 18 . 9 ] , ... , [ 20 . 1 , 20 . 2 ] (15 bins) ◮ Statistical uncertainties approximated as Gaussian ◮ Systematic uncertainty on E : ± 14 % The composition (PRD 90 (2014) 122005, arXiv:1409.4809 ): ◮ log 10 ( E / eV ) bins [ 18 . 7 , 18 . 8 ] , ... , [ 19 . 4 , 19 . 5 ] , [ 19 . 5 , 20 . 0 ] (9 bins) ◮ X max / ( g / cm 2 ) bins [ 0 , 20 ] , [ 20 , 40 ] , ... , [ 1980 , 2000 ] (most empty) ◮ 110 non-empty bins in total ◮ Multinomial X max distribution in each log 10 ( E / eV ) bin ◮ Systematic uncertainty on X max : ≈ ± 8 g / cm 2 (energy-dependent) Armando di Matteo (Pierre Auger Collaboration) Combined fit of Auger spectrum and composition data 34th ICRC, The Hague (2015) 6 / 14
The best fit (SPG propagation, EPOS-LHC air interactions) J 0 = 7 . 17 × 10 18 eV − 1 Mpc − 3 yr − 1 (at 10 18 eV) ( L 0 = 5 . 15 × 10 44 erg Mpc − 3 yr − 1 total) γ = 0 . 94 + 0 . 09 − 0 . 10 R cut = 10 18 . 67 ± 0 . 03 V 0 . 0 + 29 . 9 % H, 62 . 0 + 3 . 5 − 22 . 2 % He, 37 . 2 + 4 . 2 − 12 . 6 % N, − 0 . 3 % Fe (at 10 18 eV) 0 . 8 + 0 . 2 (0.0% H, 28.9% He, 65.6% N, 5.5% Fe total) H ] ] EPOS-LHC D / n = 178 . 5 / 119 ( D J = 18 . 8, D X max = 159 . 8) -2 850 -2 He [g cm ) [g cm 60 H N 800 Fe p = 0 . 026 〉 750 He max max 40 X (X 700 〈 N σ 650 20 Fe 18 18.5 19 19.5 20 18 18.5 19 19.5 20 log (E/eV) log (E/eV) 10 10 Armando di Matteo (Pierre Auger Collaboration) Combined fit of Auger spectrum and composition data 34th ICRC, The Hague (2015) 7 / 14
Comments on the result Hard, metal-rich injection, as also found by: ◮ R. Aloisio, V. Berezinsky and P. Blasi [ arXiv:1312.7459 ] ◮ A. Taylor, M. Ahlers and D. Hooper [ arXiv:1505.06090 ], unless source density increases with decreasing redshift ◮ N. Globus, D. Allard and E. Parizot [ arXiv:1505.01377 ] Results mainly due to narrow X max distributions → little mixing of different masses at the same energy Armando di Matteo (Pierre Auger Collaboration) Combined fit of Auger spectrum and composition data 34th ICRC, The Hague (2015) 8 / 14
Likelihood plot (SPG propagation, EPOS-LHC air interactions) D - D min 12 /V) 20.5 350 cut 10 (R 20 300 10 log 250 8 19.5 200 -1 0 1 2 6 19 γ 4 18.5 2 18 0 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 γ Armando di Matteo (Pierre Auger Collaboration) Combined fit of Auger spectrum and composition data 34th ICRC, The Hague (2015) 9 / 14
2nd local minimum (SPG propagation, EPOS-LHC air interactions) J 0 = 4 . 53 × 10 19 eV − 1 Mpc − 3 yr − 1 (at 10 18 eV) γ = 2 . 03 R cut = 10 19 . 84 V 0 . 0 % H, 0 . 0 % He, 94 . 2 % N, 5 . 8 % Fe (at 10 18 eV) D / n = 235 . 0 / 119 ( D J = 14 . 5, D X max = 220 . 5) p = 5 × 10 − 4 H ] EPOS-LHC -2 850 He [g cm N 800 disfavoured at the 7 . 5 σ level Fe 〉 750 max X 700 〈 650 18 18.5 19 19.5 20 log (E/eV) 10 Armando di Matteo (Pierre Auger Collaboration) Combined fit of Auger spectrum and composition data 34th ICRC, The Hague (2015) 10 / 14
Dependence on propagation models Analysis repeated with other propagation models Models with lower interaction rates favoured The higher the interaction rates, the lower the injection cutoff and spectral index Armando di Matteo (Pierre Auger Collaboration) Combined fit of Auger spectrum and composition data 34th ICRC, The Hague (2015) 11 / 14
Dependence on energy and X max scale Analysis repeated shifting E and/or X max by their syst. uncertainties Lowered energy and (to a lesser extent) X max scales favoured The deeper the showers, the harder the required injection spectrum Armando di Matteo (Pierre Auger Collaboration) Combined fit of Auger spectrum and composition data 34th ICRC, The Hague (2015) 12 / 14
Dependence on UHECR-air interaction models Analysis repeated with other air interaction models EPOS-LHC favoured, QGSJet II-04 disfavoured Sibyll 2.1 and QGSJet II-04 require extremely hard injection spectra Armando di Matteo (Pierre Auger Collaboration) Combined fit of Auger spectrum and composition data 34th ICRC, The Hague (2015) 13 / 14
Conclusions Hard injection ( γ � 1) with low cutoff ( R cut � 10 18 . 7 V) favoured Qualitatively similar results for all models, but model-dependent best-fit parameter values γ ≈ 2 injection much less sensitive on propagation details, but strongly disfavoured by X max distribution width Lowered energy and (to a lesser extent) X max scales favoured EPOS-LHC favoured over Sibyll 2.1 and QGSJet II-04 Journal paper in preparation Armando di Matteo (Pierre Auger Collaboration) Combined fit of Auger spectrum and composition data 34th ICRC, The Hague (2015) 14 / 14
Back-up slides Simple exponential cutoff 4 X max distributions 5 Armando di Matteo (Pierre Auger Collaboration) Combined fit of Auger spectrum and composition data 34th ICRC, The Hague (2015) 1 / 4
Simple exponential cutoff D - D min 12 /V) 20.5 300 cut 10 (R 20 250 10 log 8 19.5 200 -1 0 1 2 6 19 γ 4 18.5 2 18 0 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 γ best fit 2nd min D ( J ) D ( J ) cutoff γ R cut / V D min γ R cut / V D D ( X max ) D ( X max ) 0 . 94 + 0 . 09 14 . 5 10 18 . 67 ± 0 . 03 18 . 8 10 19 . 84 broken exp 178 . 5 2.03 235 . 0 − 0 . 10 159 . 8 220 . 5 10 18 . 63 + 0 . 09 0 . 53 + 0 . 21 17 . 3 10 19 . 94 14 . 6 simple exp 177.2 1.89 221.0 − 0 . 06 − 0 . 18 159 . 9 206 . 5 Armando di Matteo (Pierre Auger Collaboration) Combined fit of Auger spectrum and composition data 34th ICRC, The Hague (2015) 2 / 4
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